Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
import math
n=int(input())
s=(2*n)**0.5
x=math.ceil(s)
i=1
j=x
c=0
while i<=j:
    if (j*(j+1)//2)+(i*(i+1)//2)>n:
        j-=1
    elif (j*(j+1)//2)+(i*(i+1)//2)<n:
        i+=1
    elif (j*(j+1)//2)+(i*(i+1)//2)==n:
        print('YES')
        c+=1
        break
if c==0:
    print('NO')